From the Two Together FAQs:
"Can I use the Two Together Railcard when I am travelling on my own?
No. The Railcard is for use by you and the second named adult on your Railcard when you are travelling together. The two named cardholders must travel together for the entire journey for their discounted tickets to be valid."
https://www.twotogether-railcard.co.uk/help/faqs/279/
It seems quite clear, if the two passengers do not travel together for the whole journey the tickets are not valid. Whatever anyone thinks of rail travel TOCs, they are there and have to adhered to (and that works for both sides of the contract). If the rules start to get relaxed, people will find ways to abuse them and before you know it they will disappear.
Following the strictest reading of:
The two named cardholders must travel together for the entire journey for their discounted tickets to be valid.
Would imply that the two people cannot be separated on their journey for any reason, as such one cannot go to the buffet or loo without the other.
It could also be read that is they arrive at the station (as that is part of their journey) separately their tickets would also be invalid.
Given that both of the above are permitted it would imply that the train for the rule is to ensure that the discount is only applied when purchasing two tickets and that both tickets must be in use on the same train.
The only possible advantage that I can see is that by booking more than one seat you encourage others to use another service and so maybe it would result in a few less people on the train you are on. However there would need to be a lot of people doing so to make it worth people doing it.
In the other side of the coin, the TOC's benefit by there being less advanced tickets for sale for use by other passengers. This would likely result in then having a larger income (even if there was occasions where 2/3 + 2/3 = <1).
As an example I have a train with 300 seats, it would normally cost £30 to use that service. To encourage people to use my train over anyone elses I offer 100 seats at £10, followed by 200 seats at £25.
If by some fluke someone using a 2 together card gets two seats for £9, which they plan to use on their own, that then means that one more person is going to pay me £25. That means that the total those 2 people pay me £34 rather than £20.
Now it could be that by not having any more £10 tickets someone choices not to travel on my train, on which case I've only got £34 rather than £45. However normally that would be £37 out of £45, and I would have that if there were actually two people traveling anyway.
Most people who travel by train do so because they need to, not because it's cheaper. As such, as a TOC it would be in my interest to have at many people travel using two discounted tickets as possible.
Take the above train again, if 200 tickets are sold on two together but only 100 people travel, even if the two tickets were a total of £9 and £20 (rather than £10 and £25) I would sell 50 at £9 and 50 at £20. That would be 100 people on my train for £1,450 rather than £1,000 if the tickets were sold at £10 for the first 100. That would mean that even if 15 people choose not to travel (£375 "loss") I would still be better off by £75 than if everyone brought their tickets correctly. It should be noted that the only way that I'd be having those 15 people is if they managed to get one of my £10 tickets, as such there's probably not much point in trying too hard to get then to use my trains.
However in reality I would be significantly better off than that, as the two together discount would result in a £13 for 2 and £33 for 2, meaning that the income would be £2,300 (rather than the £1,450 if there was a loophole), meaning that a lot of people would need to need to choose not to travel to mean I was worse off. In fact more than 50 people, so actual it's not possible for those ticket sales to hurt me.
However I'm also left with 100 extra seats on my train meaning that more people can travel on the turn up and go basis paying the full £30.
Even if that £30 is split between other train companies the fact that my trains are emptier means that people may it to use my service (so as to get a seat) and then buy my discounted advanced tickets in the future, which benefits by business.
If I insist on all those I catch paying the £30 I would find that I would get a lot of bad publicity (harming my business) as well as only getting a share of that £30 (making those other TOC's who run a competing service a load of extra money for doing nothing, especially if I only provide, say, 10% of seats/services on that route).
As such my instructions to my staff would be; Yes charge those with only one ticket who try it on, but if they have two tickets warn them that they shouldn't be doing this but let them off. Saying other rail staff may not be so forgiving.
Likewise if you catch someone with a super off peak ticket let them buy a single until the point that the super off peak ticket becomes valid. Again saying "I shouldn't really be doing this, and you should be paying £££, but...".
In doing so I get a lot of extra income and the traveling public think that I'm a good guy, making people more likely to use my trains (and therefore making me even more money).